Question

find CSA and TSA of circular cone whose height is 2 cm and radius is 3.5 cm

Answer 1

l² = h² + r²
l² = 4 + 12.25 = 16.25
l = √16.25 = 4.03

csa = πrl = 3.14 x 4.03 x 3.5 = 44.28 cm²

tsa = πr(l+r)
=  3.14 x 3.5 (4.03 + 3.5)
= 10.99 x 7.53
= 82.75 cm²

Answer 2

$\huge{\mathcal{\underline{\purple{Solution:-}}}}$

Height of cone(h) = 2cm

Radius of cone(r) = 3.5 cm

In a cone ,

$\large\rm\bold{\boxed{l^2\:=\:r^2+h^2}}$

$\large\rm{l\rightarrow{Slant\:height\:of\:cone}}$

$\large\rm{r\rightarrow{Radius\:of\:cone}}$

$\large\rm{h\rightarrow{Height\:of\:cone}}$

$\large\rm{\implies{l^2\:=\:(3.5)^2+(2)^2}}$

$\large\rm{\implies{l^2\:=\:16.25}}$

$\large\rm{\implies{l\:=\:\sqrt{16.25}\:=\:4.0}}$

$\large\rm\bold{\boxed{CSA\:of\:cone\:=\:πrl}}$

$\large\rm{r\rightarrow{Radius\:of\:cone}}$

$\large\rm{l\rightarrow{slant\:height\:of\:cone}}$

$\large\rm{CSA\:=\:\frac{22}{7}\times\:3.5\times\:2}$

$\large\rm{\implies{CSA\:=\:22 cm^2}}$

TSA of cone is given by ,

$\large\rm\bold{\boxed{TSA\:=\:πr(r+l)}}$

$\large\rm{r\rightarrow{Radius\:of\:cone}}$

$\large\rm{l\rightarrow{Slant\:height\:of\:cone}}$

$\large\rm{TSA\:=\:\frac{22}{7}\times\:3.5(3.5+4)}$

$\large\rm{\implies{TSA\:=\:11(7.5)}}$

$\large\rm{\implies{TSA\:=\:82.5\:cm^2}}$

∴ CSA of cone = 22 cm²

TSA of cone = 82.5 cm²